A numerical study is presented for three‐dimensional magnetic hybrid nanofluid (SWCNT + Ag–H2O) flow over a porous bidirectional stretchable surface due to the physical effects of a higher‐order chemical reaction, internal heat generation, and mixed convection. The systems of nonlinear ordinary diffrential equations of hybrid nanofluid that is, flow, energy, and mass transfer are developed and computations have been carried out, employing shooting method along with Runge–Kutta–Fehlberg fourth‐ and fifth‐order technique. The characteristics of heat transfer, mass diffusion, and fluid flow are presented for the range of porosity parameter,
0.5
≤
K
≤
1.2; Hartmann number,
0.2
≤
H
a
≤
1; internal heat generation,
0.1
≤
H
≤
1; thermal Grashof number,
0.1
≤
G
r
T
≤
0.4; mass Grashof number,
0.1
≤
G
r
C
≤
0.4; Schmidt number,
0.2
≤
S
c
≤
1; chemical reaction parameter,
0.5
≤
Y
≤
3, and order of chemical reaction (
1
≤
q
≤
4) for power index number
n
=
1 and 2 at a fixed value of nanoparticles' volume fraction and Prandtl number. The graphs and tables are depicted and explained for the response to various embedded parameters. The upshots of the current problem illustrate that with an increase in the magnetic field and chemical reaction, the mass transfer rate increases. Moreover, Nusselt number profiles are reduced with an increase in the coefficient of volumetric heat generation values for both power index number, that is,
n
=
1 and 2.